# Initially $\kappa $-compact spaces for large $\kappa $

Commentationes Mathematicae Universitatis Carolinae (1999)

- Volume: 40, Issue: 2, page 319-325
- ISSN: 0010-2628

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topChristodoulou, Stavros. "Initially $\kappa $-compact spaces for large $\kappa $." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 319-325. <http://eudml.org/doc/248413>.

@article{Christodoulou1999,

abstract = {This work presents some cardinal inequalities in which appears the closed pseudo-character, $\psi _c$, of a space. Using one of them — $\psi _c(X) \le 2^\{d(X)\}$ for $T_2$ spaces — we improve, from $T_3$ to $T_2$ spaces, the well-known result that initially $\kappa $-compact $T_3$ spaces are $\lambda $-bounded for all cardinals $\lambda $ such that $2^\lambda \le \kappa $. And then, using an idea of A. Dow, we prove that initially $\kappa $-compact $T_2$ spaces are in fact compact for $\kappa = 2^\{F(X)\}$, $2^\{s(X)\}$, $2^\{t(X)\}$, $2^\{\chi (X)\}$, $2^\{\psi _c(X)\}$ or $\kappa = \max \lbrace \tau ^+, \tau ^\{<\tau \}\rbrace $, where $\tau > t(p,X)$ for all $p \in X$.},

author = {Christodoulou, Stavros},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {initially $\kappa $-compact space; $\kappa $-bounded space; closed pseudocharacter; cardinal inequalities; initially -compact space; -bounded space; closed pseudocharacter for a space},

language = {eng},

number = {2},

pages = {319-325},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Initially $\kappa $-compact spaces for large $\kappa $},

url = {http://eudml.org/doc/248413},

volume = {40},

year = {1999},

}

TY - JOUR

AU - Christodoulou, Stavros

TI - Initially $\kappa $-compact spaces for large $\kappa $

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1999

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 40

IS - 2

SP - 319

EP - 325

AB - This work presents some cardinal inequalities in which appears the closed pseudo-character, $\psi _c$, of a space. Using one of them — $\psi _c(X) \le 2^{d(X)}$ for $T_2$ spaces — we improve, from $T_3$ to $T_2$ spaces, the well-known result that initially $\kappa $-compact $T_3$ spaces are $\lambda $-bounded for all cardinals $\lambda $ such that $2^\lambda \le \kappa $. And then, using an idea of A. Dow, we prove that initially $\kappa $-compact $T_2$ spaces are in fact compact for $\kappa = 2^{F(X)}$, $2^{s(X)}$, $2^{t(X)}$, $2^{\chi (X)}$, $2^{\psi _c(X)}$ or $\kappa = \max \lbrace \tau ^+, \tau ^{<\tau }\rbrace $, where $\tau > t(p,X)$ for all $p \in X$.

LA - eng

KW - initially $\kappa $-compact space; $\kappa $-bounded space; closed pseudocharacter; cardinal inequalities; initially -compact space; -bounded space; closed pseudocharacter for a space

UR - http://eudml.org/doc/248413

ER -

## References

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